Verified solution · Exam FM

SOA Exam FM Sample Question #262 Solution

This Exam FM sample reference tests Annuities. At time 5 the payments are 1,000 through 3,000, which decompose into a 500 level annuity-due plus 500 times an increasing annuity-due. Discounting that time-5 value by v to the fifth gives the expression in choice D.

Independent analysis by ActuaryProof · reviewed August 4, 2026

Official wording withheld. Read the problem in the official SOA sample-question PDF. This page provides only our independently written analysis.

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Independent solution

How to solve this Annuities question

Setup

Use time 5, the date of the first payment, as the local valuation date.

(1000,1500,2000,2500,3000)=500(1,1,1,1,1)+500(1,2,3,4,5)

Model

Both local streams begin immediately at time 5, so they are annuities-due.

V_5=500\ddot a_{\overline5|i}+500(I\ddot a)_{\overline5|i}

Compute

Bring the local value back five years to time 0.

V_0=v^5\left[500\ddot a_{\overline5|i}+500(I\ddot a)_{\overline5|i}\right]

Answer

This formula is exactly the expression in choice D.

\boxed{\text{choice D}}

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Error diagnosis

Why the other letters tempt

These notes identify the calculation error associated with each wrong letter when that error is reproducible.

AChoice A does not satisfy the time-5 annuity-due decomposition followed by five years of discounting; no distinct standard one-step error is identifiable.
BChoice B does not satisfy the time-5 annuity-due decomposition followed by five years of discounting; no distinct standard one-step error is identifiable.
CChoice C does not satisfy the time-5 annuity-due decomposition followed by five years of discounting; no distinct standard one-step error is identifiable.
EChoice E does not satisfy the time-5 annuity-due decomposition followed by five years of discounting; no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: present value of a deferred arithmetic grant stream

A five-payment grant begins with 600 at year 3, and each later annual payment is 200 larger. At a 5% annual effective yield, calculate the present value at time 0.

A
3,657.88
B
3,850.40
C
4,042.92
D
4,235.44
E
4,427.96

Variant answer in brief

Discounting the five payments 600 through 1,400 from years 3 through 7 gives present value 3,850.40, choice B.

Setup

Generate the five payment amounts and their dates.

P_k=600+200k,\qquad t_k=3+k,\qquad k=0,\ldots,4

Model

Discount every payment directly to time 0 at 5%.

PV=\sum_{k=0}^{4}(600+200k)(1.05)^{-(3+k)}

Compute

The five-term discounted sum is 3850.403044.

PV=3850.40304357

Answer

The grant's present value is 3,850.40, selecting choice B.

\boxed{PV\approx3850.40\quad\text{(B)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #262 — Verified Solution.” Verified 2026-07-31.

Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.

How to solve this Annuities question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: present value of a deferred arithmetic grant stream

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution